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Security of Pseudo-Random Number Generators with Input

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Innovative Security Solutions for Information Technology and Communications (SecITC 2017)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 10543))

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Abstract

A pseudo-random number generator is a deterministic algorithm that produces numbers whose distribution is indistinguishable from uniform. A formal security model for pseudo-random number generator with input was proposed in 2005 by Barak and Halevi. This model involves an internal state that is refreshed with a (potentially biased) external random source, and a cryptographic function that outputs random numbers from the internal state. We briefly discuss the Barak-Halevi model and its extension proposed in 2013 by Dodis, Pointcheval, Ruhault, Wichs and Vergnaud to include a new security property capturing how a pseudo-random number generator should accumulate the entropy of the input data into the internal state. This property states that a pseudo-random number generator with input should be able to eventually recover from compromise even if the entropy is injected into the system at a very slow pace, and expresses the real-life expected behavior of existing designs. We also outline some variants of this model that were proposed recently.

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Notes

  1. 1.

    OpenSSL 0.9.8c-1 up to versions before 0.9.8g-9.

  2. 2.

    In a similar setting, Koshiba [Kos02] proved that the linear congruential generator can be used to generate randomness in the ElGamal encryption scheme (based on some plausible assumption). Fouque, Tibouchi, and Zapalowicz [FTZ13] analyzed the security of public-key schemes when the secret keys are constructed by concatenating the outputs of a linear congruential generator. Benhamouda, Chevalier, Thillard and Vergnaud [BCTV16] proposed attacks when the RSA prime factors are constructed in this way and against the RSA encryption padding described in PKCS #1 v.1.5 when a linear congruential generator is used to generate random values.

  3. 3.

    Gazi and Tessaro proposed a variant of a construction proposed by Bertoni, Daemen, Peeters and Van Assche in [BDPV10] and proved that it achieves robustness in a variant of the security framework of Dodis et al. in the ideal permutation model.

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Acknowledgments

The author would like to thank his co-authors on this active and interesting research area: Michel Abdalla, Sonia Belaïd, Yevgeniy Dodis, David Pointcheval, Sylvain Ruhault and Daniel Wichs.

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Authors and Affiliations

  1. Département d’informatique de l’ENS, École normale supérieure, CNRS, PSL Research University, 75005, Paris, France

    Damien Vergnaud

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  1. Damien Vergnaud
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Correspondence to Damien Vergnaud .

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Editors and Affiliations

  1. École Normale Supérieure, Paris, France

    Pooya Farshim

  2. Polytechnic University of Bucharest, Bucharest, Romania

    Emil Simion

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Vergnaud, D. (2017). Security of Pseudo-Random Number Generators with Input. In: Farshim, P., Simion, E. (eds) Innovative Security Solutions for Information Technology and Communications. SecITC 2017. Lecture Notes in Computer Science(), vol 10543. Springer, Cham. https://doi.org/10.1007/978-3-319-69284-5_4

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  • DOI: https://doi.org/10.1007/978-3-319-69284-5_4

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